Both of the records are known for being the respective band's commercial record, so I'd say this is a very interesting poll (not that I doubted for a second who was gonna win on this site, though).
Although TBA is probably a bit more commercial than Ritual, I'd still say TBA is the better one, 'cause I don't see TBA as a bad record. I actually like it more than Justice, that record never really grabbed me (except for the god-awesome opener, IMO one of the best songs ever).
I know, there wasn't much thrash left on TBA compared to Justice, but the riffs were still there, if not of the same thrash caliber. Instead of being all-out thrashy, the songs became much catchier, but not really in a bad way. Also, not all the speed was gone, Holier than Thou, Through the Never and Of Wolf and Man were still some fast tracks (which is likely why none of those tracks made it to being singles).
The serious lack of speed was my main issue with The Ritual, which is the main reason to why I rank it lower. Electric Crown and Return to Serenity, that's pretty much it as far as solid tracks go, IMO. TBA still had some catchiness to back up the lack of thrash, but IMO, The Ritual just didn't have it.
Maybe it's because I'm a fairly open-minded metalhead, I listen to everything from mosh-speed thrash to glam (as long as it qualifies as "metal" or "rock"). That's my two cents.